arXiv research

Currents on cusped hyperbolic surfaces have a denseness property similar to compact surfaces.

Classifies manifolds with dense conjugacy classes in their mapping class groups.

The paper explores graphons of line graphs from sparse finite graphs.

The paper explores the twisted Rokhlin property in mapping class groups of surfaces.

We prove that a dense subgroup of $\mathrm{Homeo}_{+}(I)$ is not elementary amenable. We also show that the topological group $\mathrm{Homeo}_{+}(I)$ does not satisfy the Stability of the Generators Property, moreover, any finitely generated subgroup of $\mathrm{Homeo}_{+}(I)$ admits a faithful discrete representation …

Deforms surface groups to be Zariski dense in SL(n,R)

In this paper we show that certain generalizations of the $C^r$-Whitney topology, which include the Hölder-Whitney and Sobolev-Whitney topologies on smooth manifolds, satisfy the Baire property, to wit, the countable intersection of open and dense sets is dense.

We show that the bounded Borel class of any dense representation $ρ: G\to \PSL_n\bC$ is non-zero in degree three bounded cohomology and has maximal semi-norm, for any discrete group $G$. When $n=2$, the Borel class is equal to the $3$-dimensional hyperbolic volume class. Using tools from the theory of Kleinian groups, …

A pair of points (x,y) in a Riemannian manifold (M,g) is said to have the finite blocking property if there is a finite set P contained in M\{x,y} such that every geodesic segment from x to y passes through a point of P. We show that for every closed C-infinity manifold M of dimension at least two and every pair (x,y) …

The paper finds free semigroups in dense subgroups of Lie groups with critical exponents arbitrarily close to the subgroup's.

We introduce and study the operation, called dense amalgam, which to any tuple X_1,...,X_k of non-empty compact metric spaces associates some disconnected perfect compact metric space, denoted $\widetilde\sqcup(X_1,...,X_k)$, in which there are many appropriately distributed copies of the spaces X_1,...,X_k. We then sh…

The paper shows BNSR-invariants of McCool groups are either dense or empty.

Bayesian networks are typically faithful, with implications for causal inference.

In this paper we construct a properly embedded holomorphic disc in the unit ball $\mathbb{B}^2$ of $\mathbb{C}^2$ having a surprising combination of properties: on the one hand, it has finite area and hence is the zero set of a bounded holomorphic function on $\mathbb{B}^2$; on the other hand, its boundary curve is eve…

DenseHMM improves HMMs by learning dense representations that enable gradient-based optimization.

Horizon saddle connections imply dense hyperbolic geodesics on dilation surfaces.

New subgroup found in Lie groups with unusual properties.

New GPU kernels boost deep learning speed and memory efficiency.

We study the regularity properties of the value function associated with an affine optimal control problem with quadratic cost plus a potential, for a fixed final time and initial point. Without assuming any condition on singular minimizers, we prove that the value function is continuous on an open and dense subset of …

We describe the "hyperbolic" properties of a riemann surface lamination M canonically associated to every compact three manifolds of curvature less than 1. More precisely, if the geodesic flow is the phase space attached to an ordinary differential equation, our space M is the "phase space" attached to a certain ellipt…

The square-peg problem is solved using configuration spaces and multijet transversality.

We investigate some topological properties of a normal functor $H$ introduced earlier by Radul which is some functorial compactification of the Hartman--Mycielski construction HM. We prove that the pair ($HX$, HM$Y$) is homeomorphic to the pair $(Q,σ)$ for each nondegenerated metrizable compactum $X$ and each dense $σ$…

The paper classifies extensions of Yang-Mills-type theories, proving maximality and universality are dense properties.

We discuss properties of the regular part $S_{reg}$ of a subcartesian space $S$. We show that $S_{reg}$ is open and dense in $S$ and the restriction to $S_{reg}$ of the tangent bundle of $S$ is locally trivial.

Let $M$ be a complete metric $ANR$-space such that for any metric compactum $K$ the function space $C(K,M)$ contains a dense set of Bing (resp., Krasinkiewicz) maps. It is shown that $M$ has the following property: If $f\colon X\to Y$ is a perfect surjection between metric spaces, then $C(X,M)$ with the source limitati…

Study on horospheres in higher rank homogeneous spaces, proving density properties.

Study on visibility properties of spiral sets in higher dimensions.

Study thin hyperbolic reflection groups and their properties.

Sparse Hopfield model improves memory retrieval with fewer connections.

New method estimates precision matrices without models, achieving dense, consistent, and model-free properties.

The paper proves properties of strain tensors on surfaces with changing Gauss curvature.

The paper characterizes $G$-ANR spaces and their properties.

Study irrational rotations and construct 2-filling rays on infinite type surfaces.

The Greenberg-Shalom hypothesis connects subgroup properties to lattice structures in Lie groups.

A compact Polish foliated space is considered. Part of this work studies coarsely quasi-isometric invariants of leaves in some residual saturated subset when the foliated space is transitive. In fact, we also use "equi-" versions of this kind of invariants, which means that the definition is satisfied with the same con…

Generic Hitchin representations generate dense subgroups.

We survey the construction and properties of the Yamada polynomial of spatial graphs and present the Yamada polynomial formulae for some classes of graphs. Then we construct an infinite family of spatial graphs for which roots of Yamada polynomials are dense in the complex plane.

New lattices in higher dimensions have dense surface subgroups.

Generic Hitchin representations avoid hyperplanes in Lie algebras.

We discuss dense embeddings of surface groups and fully residually free groups in topological groups. We show that a compact topological group contains a nonabelian dense free group of finite rank if and only if it contains a dense surface group. Also, we obtain a characterization of those Lie groups which admit a dens…

We study the design of learning architectures for behavioural planning in a dense traffic setting. Such architectures should deal with a varying number of nearby vehicles, be invariant to the ordering chosen to describe them, while staying accurate and compact. We observe that the two most popular representations in th…

Improvements in the performance of deep neural networks have often come through the design of larger and more complex networks. As a result, fast memory is a significant limiting factor in our ability to improve network performance. One approach to overcoming this limit is the design of sparse neural networks, which ca…

We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of this general result is illustrated by a number of examples, dealing with convex …

We prove that the Teichmueller disc stabilized by the Arnoux-Yoccoz pseudo-Anosov diffeomorphism contains at least two closed Teichmueller geodesics. This proves that the corresponding flat surface does not have a cyclic Veech group. In addition, we prove that this Teichmueller disc is dense inside the hyperelliptic lo…

Bi-Lipschitz rigidity theorem for dense subgroups of algebraic groups.

Deep-Lock secures DNN models with secret keys.

The study finds conditions for certain groups to be dense in a specific mathematical space.

Lottery tickets find good initializations for IMP with sparse training.